Nuprl Lemma : geo-seg-length-test
∀e:BasicGeometry. ∀[a,b,c,d,x,y:Point]. (ba ≅ xy) supposing (dc ≅ yx and ab ≅ cd)
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-congruent: ab ≅ cd,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
uiff: uiff(P;Q),
member: t ∈ T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
geo-point_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-congruent_wf,
geo-length-flip,
geo-congruent-iff-length
Rules used in proof :
sqequalRule,
instantiate,
applyEquality,
equalitySymmetry,
equalityTransitivity,
hypothesis,
because_Cache,
independent_isectElimination,
productElimination,
isectElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}[a,b,c,d,x,y:Point]. (ba \00D0 xy) supposing (dc \00D0 yx and ab \00D0 cd)
Date html generated:
2017_10_02-PM-06_20_56
Last ObjectModification:
2017_08_05-PM-04_15_27
Theory : euclidean!plane!geometry
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